Complicated simple question - ray tracing

Hello

I'm working currently on a project - I have an optical system (some prisms, some lenses etc) and I want to do a VI to calculate the propagation of a ray of light - something like ray tracing.

I know that labview is not a perfect platform to address this issue, but I still want to try.

My problem is as follows: I want to calculate the propagation of a ray through a lens. I skate with some coordinates (y = const) and a lens plano convex - forward of a lens is a piece of a sphere. To calculate the spread (using snell's law), I find an angle between the RADIUS and the line that is tangent to this sphere lens to the point where my light beam hits the lens.

My procedure (on the piece of paper):

1.i know the coordinates of the center of a sphere (take (0,0)) and its radius r (x ^ 2 + y ^ 2 = r ^ 2). I know that the value of y = y_0 including the ray enters the goal.

so I can calculate the x_0: x_0 ^ y_0 2 + ^ 2 = r ^ 2. Now, I know the point where the light enters the lens (x_0, y_0)

2. then comes the usual procedure to find the equation of a tangent line to the sphere (y = a * x + b):

I updated y_0 and x_0 this equation:

Y_0 = a * x_0 + b

and I can't remove an unknown value (e.g. b): y = a *(x-y_0) + x_0

3. then I put this assimilation into the equation of the sphere (x ^ 2 + y ^ 2 = r ^ 2) and it's the quadratic equation that have an unknown value x and only one free parameter: a.

4 beacause I want to have the tangent line, so there should be a single good with sphere - so the quadratic equation should have determinant equal to zero (the only solution for x). It gives me an equation for one. I should find the value of a that satisfies this equation and then I know this tangent line and I have the solution! UF...

Unfortunately I still have not found a solution to implement this in labview (and I'm motivated because most of the work of this project is already done). I tried with the formula of analysis and so on, but I could not.

I will be really grateful for any advice or help!

Helmik,

LabVIEW does not symbolic math.  Once you have the equations solved on paper or reduced to a set that can be solved numerically, so you can program in LV

When I look at your math in the first post, I see that (3) you describe an equation in x and a. However, this is not an order quadratic equation, but a fourth polynomial with terms like a ^ 2 * x ^ 2-2 * a ^ 2 * x * y_0. If this is not so easily resolved.

Isn't the tangent to the sphere perpendicular to the RADIUS at that time? The angle of the beam can be calculated from x_0, y_0 and the center of the sphere. Then add 90 degrees. An arc tangent and no complicated equations.

Lynn

Tags: NI Software

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